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arXiv · 1601.00861

Efficient cyclic reduction for QBDs with rank structured blocks

Dario A. Bini·Stefano Massei·Leonardo Robol
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Abstract

We provide effective algorithms for solving block tridiagonal block Toeplitz systems with $m\times m$ quasiseparable blocks, as well as quadratic matrix equations with $m\times m$ quasiseparable coefficients, based on cyclic reduction and on the technology of rank-structured matrices. The algorithms rely on the exponential decay of the singular values of the off-diagonal submatrices generated by cyclic reduction. We provide a formal proof of this decay in the Markovian framework. The results of the numerical experiments that we report confirm a significant speed up over the general algorithms, already starting with the moderately small size $m\approx 10^2$.

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Dario A. Bini, Stefano Massei, Leonardo Robol. 2016-01-05. Efficient cyclic reduction for QBDs with rank structured blocks. https://arxiv.org/abs/1601.00861

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